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Unformatted text preview: Part 6 1. Solution: Mass of car, = m1 1000 kg Velocity of car, = v1 ? Mass of truck, = m2 1600 kg Velocity of truck, = / v2 40 m s Momentum of truck = = / m2v2 1600 X 40 kgm s Momentum of car = = m1v1 1000v1 = 1000v1 1600 X 40 = = / v1 640001000 64 m s Kinetic energy of car = = = . 12m1v12 12X 1000 X 642 2 048 X 106 J Kinetic energy of truck = = = . 12m2v22 12X 1600X 402 1 28 X 106 J 2. Solution: Mass of object , = m 10 kg Constant force, = F 50 N Acceleration of object, = = = a Fm 5010 5ms2 Now, velocity of object at = t1 12 s is = / v1 5 m s Let initial velocity of object is u = + v1 u at1 .[1] Velocity of object at = t2 20 s is v2 = + v2 u at2 ..[2]  , 2 1  = =  = v2 v1 at2 t1 5 X 20 12 40 Hence, = + = / v2 v1 40 45 m s 3. Solution: Mass of rifle, = . mr 2 5 kg Recoil velocity, = vr not known Mass of bullet, = . mb 0 05 kg velocity of bullet, = / vb 200 m s towards east Lets take east to be the +ve direction. Conservation of momentum of the system at the time of firing, , + . = , + , mrvr i mbvb i mrvr f mbvb f + = , + mr0 mb0 mrvr f mb200 , = = . . = vr f mbmr200 0 052 5200 4ms Hence, recoil velocity, = / vr 4 m s towards west. 4. Solution: For the car, = , , = / , m1 500 kg v1 i 20 m s , = v1 f ? For the truck, = , , = , , = m2 2000 kg v2 i 0 v2 f ? Initial kinetic energy of the car = , = , = K1 i 12m1v1 i2 100 kJ Initial kinetic energy of truck= , = K2 i 0 Initial kinetic energy of system = = , + , = Ki K1 i K2 i 100 kJ Again, after collision, two vehicles stick together, i.e. both will move with the same vel. i.e. , = , = v1 f v2 f v Now, conservation of momentum, , + , = + m1v1 i m2v2 i m1 m2v Hence, = + + = / v 500 X 20 0500 2000 4 m s Final kinetic energy of system, = + = Kf 12m1 m2v2 20 kJ Hence, loss of kinetic energy =  = Ki Kf 80 kJ The collision is perfectly inelastic as both stick together....
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 Spring '11
 Prof.Ramachandran

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